lisc.m

LiScNLS is a Matlab application for the numerical study of some nonlinear differential equations o

function [lam,phi,phip,x,c,kod]=lisc(n,errtol,Lfun,m,Nfun,cinit)
%
% Solves two-point boundary value problems Lu=Nu
% using the Lyapunov-Schmidt method
% Reference:
% Trif, D., The Lyapunov-Schmidt method for two-point boundary value problems, 
%    Fixed Point Theory, 6,1,2005, pp. 119-132
%
disp('Linear part');
[lam,phi,phip,x,wint,wipr,dom]=sp(Lfun,n,errtol);
disp('Nonlinear part');
c0=zeros(size(lam));t=cputime;
if nargin==6
c0(1:length(cinit))=cinit;
end
for j=1:25
        [c,rez,drez,kod]=as(lam,phi,phip,x,wint,wipr,dom,c0,m,errtol,Nfun);
        if kod==-2 disp('No convergence in fixed point iterations; increase m or change c0');break;end
        if kod==-1 disp('Slow convergence in fixed point iterations; increase m');break;end
        if m==0 j=0;break;end;
        difc=-drez\rez;cor(j)=norm(difc);
        if cor(j)<errtol 
            if j<=2 break;
            else figure(1);plot(cor(2:j)./cor(1:j-1));title('Newton iterations: corrections ratio');grid;break;
            end
        end
        if (j>3 & cor(j)>=cor(j-1) & cor(j-1)>=cor(j-2)) 
            kod=-4;disp('No convergence in Newton iterations; change c0');
            figure(1);plot(cor(2:j)./cor(1:j-1));title('Newton iterations: corrections ratio');grid;
            return
        end
        c0=c;c0(1:m)=c0(1:m)+difc(1:m);
end
disp([num2str(j),' Newton iterations computed by lisc in ',num2str(cputime-t),' sec']);
if j==25 
    disp('Slow convergence in Newton iterations; change c0');kod=-3;
    figure(1);plot(cor(2:j)./cor(1:j-1));title('Newton iterations: corrections ratio');grid;
    return;
end
if (kod<0) return;end
figure(2);plot(x,phi*c);title('Solution');grid;